Question

Given that x = R cos theta , y = R sine theta and theta = wt, where R and are constants. Find the value of [(dx/dt)² + (dy/dt)²]​¹/²

Answer 1

Answer:

Rw

Explanation:

x= R cos theta

X = r cos wt

dx/ dt = - Rw sinwt

Y= R sin theta

y = R w cos wt

${ \frac{dx}{dt} }^{2}$

Answer 2

Answer:

Rw

Explanation:

x = R cos (wt) and y = R sin (wt), as θ= wt

$\frac{dx}{dt}$= R × -sin(wt) × w = -Rw × sin(wt)

$\frac{dy}{dt}$ = R × cos(wt) x w = Rw × cos(wt)

plugging these into [(dx/dt)² + (dy/dt)²]​¹/²

= {[-Rw × sin(wt)]² + [Rw × cos(wt)]²}^1/2

= {R²w² × sin²(wt) + R²w² × cos²(wt)}^1/2

= {R²w²[ sin²(wt) + cos²(wt) ]}^1/2

= {R²w² × 1}^1/2

= $\sqrt{R^{2}w^{2} }$ = Rw